From a distance the object bobbing in the bay looked like a coconut or a loose buoy, but when it was washed up on the beach it proved to be a human head.

"It wasn't pretty, not pretty at all," said José Vargas, a local waiter who joined the crowd that had gathered. He was shocked but not surprised by the grisly sight. "This kind of thing happens in Acapulco these days. I wonder when the body will show up."

Acapulco - the once glittering resort graced by Hollywood luminaries and romancing US presidents - is earning a reputation as the latest stage for an escalating turf war between Mexico's main drug cartels. Sporadic ambushes and assassinations carried out with hand grenades began in 2005, alongside a constant trickle of lower profile murders of the foot soldiers in the conflict. Now the violence is intensifying to the point that every day there is at least one death thought to be associated with the war.

"We have been seeing the violence get worse, and everything indicates we are going to carry on in this direction," the head of the state police, General Juan Heriberto Salinas, said.

Two drug cartels - one run by Joaquín "El Chapo" Guzmán, the chief of the hit squad known as Los Pelones, and the other by Osiel Cárdenas who runs a band of his own assassins, Los Zetas - are vying for control of key smuggling routes for moving South American cocaine to the US.

The cartels have been fighting it out ever since Cárdenas was captured in 2003 and El Chapo decided to make a bid for his rival's territory. The violence was once concentrated in northern cities on the Texas border, but Acapulco is now one of the hottest turfs in the country. Authorities believe the rancour of the battle goes deeper than greed.

But in Acapulco the police have also been directly involved in much of the highest profile violence, something the general accepts implies that the authorities are infiltrated by the traffickers. The most dramatic episode was a furious battle at a busy crossroads in late January between about 60 municipal police and a small caravan of heavily armed traffickers from El Chapo's group. The shooting lasted almost an hour during which one of the smugglers' cars exploded, another crashed into the side of a church and a third got away. When it was over, four traffickers lay dead amid the smouldering debris, including one of El Chapo's right-hand men.

Beheaded

In April two heads were hung in front of a government office at the same crossroads, one belonging to a high ranking policeman who had been in the combat. A sign underneath read: "Learn some respect."

As a relatively well-connected city in an otherwise largely underdeveloped stretch of coastline, in a state where isolated sierras provide perfect cover for the production of marijuana and opium paste, Acapulco is no stranger to traffickers. For years locals have told stories about cocaine washing up along the coast, with some even telling of major cargoes calmly smuggled into coves inside Acapulco city itself. Some of the mansions that speckle the cliffs around the bay are also, many surmise, just the kind of place a drug baron might like to spend a little time.

Members of the local elite remember how in the 1980s Colombians with large amounts of money of dubious origin seduced the jetset crowd with their worldly charm and fabulous parties.

A few years ago these were replaced, they say, by a rather less sophisticated and largely Mexican group. Working-class local women began turning up in exclusive shops to kit out their new homes with expensive furniture and pay for it all with large wads of cash.

At first, one society figure said, the newcomers and their gaudy taste were ignored, but that changed when the violence took off and they are now seen at the best restaurants and social events. There have even been reputed sightings of El Chapo himself.

"Now you go to children's party and there they are," she said. "People are scared that if they don't invite them there could be reprisals."

The authorities are accused of doing nothing, and rich and poor alike scoff at the special anti-drug operations dubbed "Safe Mexico". Locals say the crackdown, which includes patrols through the city, has had little significant impact beyond pushing drug dealers for local consumption to be more discreet.

The programme was first mounted in the north with the inclusion of the army, but was toned down for Acapulco for fear of frightening away the tourists that are its legal lifeblood.

Brassy

Acapulco today survives as the brash and brassy resort of choice for the lower income armies from Mexico City, five hours' bus ride away. Locals, meanwhile, are getting ever more frightened of getting caught in the crossfire and so are more than likely to avoid having anything to do with the police.

Delia Polanco spent the big January shootout cowering inside her flimsy sheet metal kiosk with her 15-year-old daughter. "We lay there trembling, listening to the assault rifles thinking it would never stop," she recalled. "If they have to fight their war why don't they do it somewhere else."

Back on the beach many holiday-makers say that despite the turf war they will keep coming to the city. "We've been coming here all our lives," 22-year-old Desiré Rojas said. "Whatever they say about Acapulco, for me it is still the best. It is the place you have the most fun."

Gen Salinas, the police chief, said: "I am an optimist and I believe we can professionalise the police force, dignify what it does and get the situation under control. But, I wouldn't like to speculate when this might happen."

Guns and glamour

· Hollywood discovered Acapulco as a backdrop at the end of the second world war, with Orson Welles using the old town centre for The Lady from Shanghai (1947)

· In 1950 the "Hollywood Gang" (John Wayne, Johnny Weissmuller, Cary Grant, Errol Flynn and others) bought the clifftop Los Flamingos Hotel and Hollywood royalty began beating a trail down to the resort, then a small town in the corner of a beautiful Pacific Bay surrounded by cliffs

· John F Kennedy went on honeymoon to Acapulco with acqueline Lee Bouvier in 1953 and Elizabeth Taylor, married Mike Todd there in 1957

· Gabriel García Márquez crystallised his idea for One Hundred Years of Solitude driving to Acapulco in 1965

· Bill Clinton honeymooned with Hillary in 1975, during a period when mass American tourism brought high-rise hotels. The glamour had faded by the 80s but there was still a jet set crowd to keep up its reputation

· Today Acapulco still has some very expensive areas, and there are efforts at a nostalgia revival, but it is predominantly the main holiday destination for the masses from Mexico City